/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date:        19. March 2015
* $Revision: 	V.1.4.5
*
* Project: 	    CMSIS DSP Library
* Title:	    arm_cfft_radix4_q31.c
*
* Description:	This file has function definition of Radix-4 FFT & IFFT function and
*				In-place bit reversal using bit reversal table
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*   - Redistributions of source code must retain the above copyright
*     notice, this list of conditions and the following disclaimer.
*   - Redistributions in binary form must reproduce the above copyright
*     notice, this list of conditions and the following disclaimer in
*     the documentation and/or other materials provided with the
*     distribution.
*   - Neither the name of ARM LIMITED nor the names of its contributors
*     may be used to endorse or promote products derived from this
*     software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
* -------------------------------------------------------------------- */

#include "arm_math.h"

void arm_radix4_butterfly_inverse_q31(
    q31_t *pSrc,
    uint32_t fftLen,
    q31_t *pCoef,
    uint32_t twidCoefModifier);

void arm_radix4_butterfly_q31(
    q31_t *pSrc,
    uint32_t fftLen,
    q31_t *pCoef,
    uint32_t twidCoefModifier);

void arm_bitreversal_q31(
    q31_t *pSrc,
    uint32_t fftLen,
    uint16_t bitRevFactor,
    uint16_t *pBitRevTab);

/**
 * @ingroup groupTransforms
 */

/**
 * @addtogroup ComplexFFT
 * @{
 */

/**
 * @details
 * @brief Processing function for the Q31 CFFT/CIFFT.
 * @deprecated Do not use this function.  It has been superseded by \ref arm_cfft_q31 and will be removed
 * @param[in]      *S    points to an instance of the Q31 CFFT/CIFFT structure.
 * @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.
 * @return none.
 *
 * \par Input and output formats:
 * \par
 * Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.
 * Hence the output format is different for different FFT sizes.
 * The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT:
 * \par
 * \image html CFFTQ31.gif "Input and Output Formats for Q31 CFFT"
 * \image html CIFFTQ31.gif "Input and Output Formats for Q31 CIFFT"
 *
 */

void arm_cfft_radix4_q31(
    const arm_cfft_radix4_instance_q31 *S,
    q31_t *pSrc)
{
    if(S->ifftFlag == 1u)
    {
        /* Complex IFFT radix-4 */
        arm_radix4_butterfly_inverse_q31(pSrc, S->fftLen, S->pTwiddle,
                                         S->twidCoefModifier);
    }
    else
    {
        /* Complex FFT radix-4 */
        arm_radix4_butterfly_q31(pSrc, S->fftLen, S->pTwiddle,
                                 S->twidCoefModifier);
    }


    if(S->bitReverseFlag == 1u)
    {
        /*  Bit Reversal */
        arm_bitreversal_q31(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
    }

}

/**
 * @} end of ComplexFFT group
 */

/*
* Radix-4 FFT algorithm used is :
*
* Input real and imaginary data:
* x(n) = xa + j * ya
* x(n+N/4 ) = xb + j * yb
* x(n+N/2 ) = xc + j * yc
* x(n+3N 4) = xd + j * yd
*
*
* Output real and imaginary data:
* x(4r) = xa'+ j * ya'
* x(4r+1) = xb'+ j * yb'
* x(4r+2) = xc'+ j * yc'
* x(4r+3) = xd'+ j * yd'
*
*
* Twiddle factors for radix-4 FFT:
* Wn = co1 + j * (- si1)
* W2n = co2 + j * (- si2)
* W3n = co3 + j * (- si3)
*
*  Butterfly implementation:
* xa' = xa + xb + xc + xd
* ya' = ya + yb + yc + yd
* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)
* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)
* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)
*
*/

/**
 * @brief  Core function for the Q31 CFFT butterfly process.
 * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.
 * @param[in]      fftLen           length of the FFT.
 * @param[in]      *pCoef           points to twiddle coefficient buffer.
 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
 * @return none.
 */

void arm_radix4_butterfly_q31(
    q31_t *pSrc,
    uint32_t fftLen,
    q31_t *pCoef,
    uint32_t twidCoefModifier)
{
#if defined(ARM_MATH_CM7)
    uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
    q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;

    q31_t xa, xb, xc, xd;
    q31_t ya, yb, yc, yd;
    q31_t xa_out, xb_out, xc_out, xd_out;
    q31_t ya_out, yb_out, yc_out, yd_out;

    q31_t *ptr1;
    q63_t xaya, xbyb, xcyc, xdyd;
    /* Total process is divided into three stages */

    /* process first stage, middle stages, & last stage */


    /* start of first stage process */

    /*  Initializations for the first stage */
    n2 = fftLen;
    n1 = n2;
    /* n2 = fftLen/4 */
    n2 >>= 2u;
    i0 = 0u;
    ia1 = 0u;

    j = n2;

    /*  Calculation of first stage */
    do
    {
        /*  index calculation for the input as, */
        /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
        i1 = i0 + n2;
        i2 = i1 + n2;
        i3 = i2 + n2;

        /* input is in 1.31(q31) format and provide 4 guard bits for the input */

        /*  Butterfly implementation */
        /* xa + xc */
        r1 = (pSrc[(2u * i0)] >> 4u) + (pSrc[(2u * i2)] >> 4u);
        /* xa - xc */
        r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);

        /* xb + xd */
        t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);

        /* ya + yc */
        s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
        /* ya - yc */
        s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);

        /* xa' = xa + xb + xc + xd */
        pSrc[2u * i0] = (r1 + t1);
        /* (xa + xc) - (xb + xd) */
        r1 = r1 - t1;
        /* yb + yd */
        t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);

        /* ya' = ya + yb + yc + yd */
        pSrc[(2u * i0) + 1u] = (s1 + t2);

        /* (ya + yc) - (yb + yd) */
        s1 = s1 - t2;

        /* yb - yd */
        t1 = (pSrc[(2u * i1) + 1u] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
        /* xb - xd */
        t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);

        /*  index calculation for the coefficients */
        ia2 = 2u * ia1;
        co2 = pCoef[ia2 * 2u];
        si2 = pCoef[(ia2 * 2u) + 1u];

        /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
        pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
                         ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;

        /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
        pSrc[(2u * i1) + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
                                ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;

        /* (xa - xc) + (yb - yd) */
        r1 = r2 + t1;
        /* (xa - xc) - (yb - yd) */
        r2 = r2 - t1;

        /* (ya - yc) - (xb - xd) */
        s1 = s2 - t2;
        /* (ya - yc) + (xb - xd) */
        s2 = s2 + t2;

        co1 = pCoef[ia1 * 2u];
        si1 = pCoef[(ia1 * 2u) + 1u];

        /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
        pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
                         ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;

        /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
        pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
                                ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;

        /*  index calculation for the coefficients */
        ia3 = 3u * ia1;
        co3 = pCoef[ia3 * 2u];
        si3 = pCoef[(ia3 * 2u) + 1u];

        /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
        pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
                         ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;

        /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
        pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
                                ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;

        /*  Twiddle coefficients index modifier */
        ia1 = ia1 + twidCoefModifier;

        /*  Updating input index */
        i0 = i0 + 1u;

    }
    while(--j);

    /* end of first stage process */

    /* data is in 5.27(q27) format */


    /* start of Middle stages process */


    /* each stage in middle stages provides two down scaling of the input */

    twidCoefModifier <<= 2u;


    for (k = fftLen / 4u; k > 4u; k >>= 2u)
    {
        /*  Initializations for the first stage */
        n1 = n2;
        n2 >>= 2u;
        ia1 = 0u;

        /*  Calculation of first stage */
        for (j = 0u; j <= (n2 - 1u); j++)
        {
            /*  index calculation for the coefficients */
            ia2 = ia1 + ia1;
            ia3 = ia2 + ia1;
            co1 = pCoef[ia1 * 2u];
            si1 = pCoef[(ia1 * 2u) + 1u];
            co2 = pCoef[ia2 * 2u];
            si2 = pCoef[(ia2 * 2u) + 1u];
            co3 = pCoef[ia3 * 2u];
            si3 = pCoef[(ia3 * 2u) + 1u];
            /*  Twiddle coefficients index modifier */
            ia1 = ia1 + twidCoefModifier;

            for (i0 = j; i0 < fftLen; i0 += n1)
            {
                /*  index calculation for the input as, */
                /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
                i1 = i0 + n2;
                i2 = i1 + n2;
                i3 = i2 + n2;

                /*  Butterfly implementation */
                /* xa + xc */
                r1 = pSrc[2u * i0] + pSrc[2u * i2];
                /* xa - xc */
                r2 = pSrc[2u * i0] - pSrc[2u * i2];

                /* ya + yc */
                s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
                /* ya - yc */
                s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

                /* xb + xd */
                t1 = pSrc[2u * i1] + pSrc[2u * i3];

                /* xa' = xa + xb + xc + xd */
                pSrc[2u * i0] = (r1 + t1) >> 2u;
                /* xa + xc -(xb + xd) */
                r1 = r1 - t1;

                /* yb + yd */
                t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
                /* ya' = ya + yb + yc + yd */
                pSrc[(2u * i0) + 1u] = (s1 + t2) >> 2u;

                /* (ya + yc) - (yb + yd) */
                s1 = s1 - t2;

                /* (yb - yd) */
                t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
                /* (xb - xd) */
                t2 = pSrc[2u * i1] - pSrc[2u * i3];

                /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
                pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
                                 ((int32_t) (((q63_t) s1 * si2) >> 32))) >> 1u;

                /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
                pSrc[(2u * i1) + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
                                        ((int32_t) (((q63_t) r1 * si2) >> 32))) >> 1u;

                /* (xa - xc) + (yb - yd) */
                r1 = r2 + t1;
                /* (xa - xc) - (yb - yd) */
                r2 = r2 - t1;

                /* (ya - yc) -  (xb - xd) */
                s1 = s2 - t2;
                /* (ya - yc) +  (xb - xd) */
                s2 = s2 + t2;

                /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
                pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
                                 ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;

                /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
                pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
                                        ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;

                /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
                pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
                                 ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;

                /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
                pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
                                        ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
            }
        }
        twidCoefModifier <<= 2u;
    }
#else
    uint32_t n1, n2, ia1, ia2, ia3, i0, j, k;
    q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;

    q31_t xa, xb, xc, xd;
    q31_t ya, yb, yc, yd;
    q31_t xa_out, xb_out, xc_out, xd_out;
    q31_t ya_out, yb_out, yc_out, yd_out;

    q31_t *ptr1;
    q31_t *pSi0;
    q31_t *pSi1;
    q31_t *pSi2;
    q31_t *pSi3;
    q63_t xaya, xbyb, xcyc, xdyd;
    /* Total process is divided into three stages */

    /* process first stage, middle stages, & last stage */


    /* start of first stage process */

    /*  Initializations for the first stage */
    n2 = fftLen;
    n1 = n2;
    /* n2 = fftLen/4 */
    n2 >>= 2u;

    ia1 = 0u;

    j = n2;

    pSi0 = pSrc;
    pSi1 = pSi0 + 2 * n2;
    pSi2 = pSi1 + 2 * n2;
    pSi3 = pSi2 + 2 * n2;

    /*  Calculation of first stage */
    do
    {
        /* input is in 1.31(q31) format and provide 4 guard bits for the input */

        /*  Butterfly implementation */
        /* xa + xc */
        r1 = (pSi0[0] >> 4u) + (pSi2[0] >> 4u);
        /* xa - xc */
        r2 = (pSi0[0] >> 4u) - (pSi2[0] >> 4u);

        /* xb + xd */
        t1 = (pSi1[0] >> 4u) + (pSi3[0] >> 4u);

        /* ya + yc */
        s1 = (pSi0[1] >> 4u) + (pSi2[1] >> 4u);
        /* ya - yc */
        s2 = (pSi0[1] >> 4u) - (pSi2[1] >> 4u);

        /* xa' = xa + xb + xc + xd */
        *pSi0++ = (r1 + t1);
        /* (xa + xc) - (xb + xd) */
        r1 = r1 - t1;
        /* yb + yd */
        t2 = (pSi1[1] >> 4u) + (pSi3[1] >> 4u);

        /* ya' = ya + yb + yc + yd */
        *pSi0++ = (s1 + t2);

        /* (ya + yc) - (yb + yd) */
        s1 = s1 - t2;

        /* yb - yd */
        t1 = (pSi1[1] >> 4u) - (pSi3[1] >> 4u);
        /* xb - xd */
        t2 = (pSi1[0] >> 4u) - (pSi3[0] >> 4u);

        /*  index calculation for the coefficients */
        ia2 = 2u * ia1;
        co2 = pCoef[ia2 * 2u];
        si2 = pCoef[(ia2 * 2u) + 1u];

        /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
        *pSi1++ = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
                   ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;

        /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
        *pSi1++ = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
                   ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;

        /* (xa - xc) + (yb - yd) */
        r1 = r2 + t1;
        /* (xa - xc) - (yb - yd) */
        r2 = r2 - t1;

        /* (ya - yc) - (xb - xd) */
        s1 = s2 - t2;
        /* (ya - yc) + (xb - xd) */
        s2 = s2 + t2;

        co1 = pCoef[ia1 * 2u];
        si1 = pCoef[(ia1 * 2u) + 1u];

        /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
        *pSi2++ = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
                   ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;

        /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
        *pSi2++ = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
                   ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;

        /*  index calculation for the coefficients */
        ia3 = 3u * ia1;
        co3 = pCoef[ia3 * 2u];
        si3 = pCoef[(ia3 * 2u) + 1u];

        /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
        *pSi3++ = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
                   ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;

        /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
        *pSi3++ = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
                   ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;

        /*  Twiddle coefficients index modifier */
        ia1 = ia1 + twidCoefModifier;

    }
    while(--j);

    /* end of first stage process */

    /* data is in 5.27(q27) format */


    /* start of Middle stages process */


    /* each stage in middle stages provides two down scaling of the input */

    twidCoefModifier <<= 2u;


    for (k = fftLen / 4u; k > 4u; k >>= 2u)
    {
        /*  Initializations for the first stage */
        n1 = n2;
        n2 >>= 2u;
        ia1 = 0u;

        /*  Calculation of first stage */
        for (j = 0u; j <= (n2 - 1u); j++)
        {
            /*  index calculation for the coefficients */
            ia2 = ia1 + ia1;
            ia3 = ia2 + ia1;
            co1 = pCoef[ia1 * 2u];
            si1 = pCoef[(ia1 * 2u) + 1u];
            co2 = pCoef[ia2 * 2u];
            si2 = pCoef[(ia2 * 2u) + 1u];
            co3 = pCoef[ia3 * 2u];
            si3 = pCoef[(ia3 * 2u) + 1u];
            /*  Twiddle coefficients index modifier */
            ia1 = ia1 + twidCoefModifier;

            pSi0 = pSrc + 2 * j;
            pSi1 = pSi0 + 2 * n2;
            pSi2 = pSi1 + 2 * n2;
            pSi3 = pSi2 + 2 * n2;

            for (i0 = j; i0 < fftLen; i0 += n1)
            {
                /*  Butterfly implementation */
                /* xa + xc */
                r1 = pSi0[0] + pSi2[0];

                /* xa - xc */
                r2 = pSi0[0] - pSi2[0];


                /* ya + yc */
                s1 = pSi0[1] + pSi2[1];

                /* ya - yc */
                s2 = pSi0[1] - pSi2[1];


                /* xb + xd */
                t1 = pSi1[0] + pSi3[0];


                /* xa' = xa + xb + xc + xd */
                pSi0[0] = (r1 + t1) >> 2u;
                /* xa + xc -(xb + xd) */
                r1 = r1 - t1;

                /* yb + yd */
                t2 = pSi1[1] + pSi3[1];

                /* ya' = ya + yb + yc + yd */
                pSi0[1] = (s1 + t2) >> 2u;
                pSi0 += 2 * n1;

                /* (ya + yc) - (yb + yd) */
                s1 = s1 - t2;

                /* (yb - yd) */
                t1 = pSi1[1] - pSi3[1];

                /* (xb - xd) */
                t2 = pSi1[0] - pSi3[0];


                /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
                pSi1[0] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
                           ((int32_t) (((q63_t) s1 * si2) >> 32))) >> 1u;

                /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
                pSi1[1] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
                           ((int32_t) (((q63_t) r1 * si2) >> 32))) >> 1u;
                pSi1 += 2 * n1;

                /* (xa - xc) + (yb - yd) */
                r1 = r2 + t1;
                /* (xa - xc) - (yb - yd) */
                r2 = r2 - t1;

                /* (ya - yc) -  (xb - xd) */
                s1 = s2 - t2;
                /* (ya - yc) +  (xb - xd) */
                s2 = s2 + t2;

                /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
                pSi2[0] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
                           ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;

                /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
                pSi2[1] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
                           ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;
                pSi2 += 2 * n1;

                /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
                pSi3[0] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
                           ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;

                /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
                pSi3[1] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
                           ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
                pSi3 += 2 * n1;
            }
        }
        twidCoefModifier <<= 2u;
    }
#endif

    /* End of Middle stages process */

    /* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
    /* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
    /* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
    /* data is in 5.27(q27) format for the 16 point as there are no middle stages */


    /* start of Last stage process */
    /*  Initializations for the last stage */
    j = fftLen >> 2;
    ptr1 = &pSrc[0];

    /*  Calculations of last stage */
    do
    {

#ifndef ARM_MATH_BIG_ENDIAN

        /* Read xa (real), ya(imag) input */
        xaya = *__SIMD64(ptr1)++;
        xa = (q31_t) xaya;
        ya = (q31_t) (xaya >> 32);

        /* Read xb (real), yb(imag) input */
        xbyb = *__SIMD64(ptr1)++;
        xb = (q31_t) xbyb;
        yb = (q31_t) (xbyb >> 32);

        /* Read xc (real), yc(imag) input */
        xcyc = *__SIMD64(ptr1)++;
        xc = (q31_t) xcyc;
        yc = (q31_t) (xcyc >> 32);

        /* Read xc (real), yc(imag) input */
        xdyd = *__SIMD64(ptr1)++;
        xd = (q31_t) xdyd;
        yd = (q31_t) (xdyd >> 32);

#else

        /* Read xa (real), ya(imag) input */
        xaya = *__SIMD64(ptr1)++;
        ya = (q31_t) xaya;
        xa = (q31_t) (xaya >> 32);

        /* Read xb (real), yb(imag) input */
        xbyb = *__SIMD64(ptr1)++;
        yb = (q31_t) xbyb;
        xb = (q31_t) (xbyb >> 32);

        /* Read xc (real), yc(imag) input */
        xcyc = *__SIMD64(ptr1)++;
        yc = (q31_t) xcyc;
        xc = (q31_t) (xcyc >> 32);

        /* Read xc (real), yc(imag) input */
        xdyd = *__SIMD64(ptr1)++;
        yd = (q31_t) xdyd;
        xd = (q31_t) (xdyd >> 32);


#endif

        /* xa' = xa + xb + xc + xd */
        xa_out = xa + xb + xc + xd;

        /* ya' = ya + yb + yc + yd */
        ya_out = ya + yb + yc + yd;

        /* pointer updation for writing */
        ptr1 = ptr1 - 8u;

        /* writing xa' and ya' */
        *ptr1++ = xa_out;
        *ptr1++ = ya_out;

        xc_out = (xa - xb + xc - xd);
        yc_out = (ya - yb + yc - yd);

        /* writing xc' and yc' */
        *ptr1++ = xc_out;
        *ptr1++ = yc_out;

        xb_out = (xa + yb - xc - yd);
        yb_out = (ya - xb - yc + xd);

        /* writing xb' and yb' */
        *ptr1++ = xb_out;
        *ptr1++ = yb_out;

        xd_out = (xa - yb - xc + yd);
        yd_out = (ya + xb - yc - xd);

        /* writing xd' and yd' */
        *ptr1++ = xd_out;
        *ptr1++ = yd_out;


    }
    while(--j);

    /* output is in 11.21(q21) format for the 1024 point */
    /* output is in 9.23(q23) format for the 256 point */
    /* output is in 7.25(q25) format for the 64 point */
    /* output is in 5.27(q27) format for the 16 point */

    /* End of last stage process */

}


/**
 * @brief  Core function for the Q31 CIFFT butterfly process.
 * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.
 * @param[in]      fftLen           length of the FFT.
 * @param[in]      *pCoef           points to twiddle coefficient buffer.
 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
 * @return none.
 */


/*
* Radix-4 IFFT algorithm used is :
*
* CIFFT uses same twiddle coefficients as CFFT Function
*  x[k] = x[n] + (j)k * x[n + fftLen/4] + (-1)k * x[n+fftLen/2] + (-j)k * x[n+3*fftLen/4]
*
*
* IFFT is implemented with following changes in equations from FFT
*
* Input real and imaginary data:
* x(n) = xa + j * ya
* x(n+N/4 ) = xb + j * yb
* x(n+N/2 ) = xc + j * yc
* x(n+3N 4) = xd + j * yd
*
*
* Output real and imaginary data:
* x(4r) = xa'+ j * ya'
* x(4r+1) = xb'+ j * yb'
* x(4r+2) = xc'+ j * yc'
* x(4r+3) = xd'+ j * yd'
*
*
* Twiddle factors for radix-4 IFFT:
* Wn = co1 + j * (si1)
* W2n = co2 + j * (si2)
* W3n = co3 + j * (si3)

* The real and imaginary output values for the radix-4 butterfly are
* xa' = xa + xb + xc + xd
* ya' = ya + yb + yc + yd
* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)
* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)
* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)
* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)
* xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)
* yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)
*
*/

void arm_radix4_butterfly_inverse_q31(
    q31_t *pSrc,
    uint32_t fftLen,
    q31_t *pCoef,
    uint32_t twidCoefModifier)
{
#if defined(ARM_MATH_CM7)
    uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
    q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
    q31_t xa, xb, xc, xd;
    q31_t ya, yb, yc, yd;
    q31_t xa_out, xb_out, xc_out, xd_out;
    q31_t ya_out, yb_out, yc_out, yd_out;

    q31_t *ptr1;
    q63_t xaya, xbyb, xcyc, xdyd;

    /* input is be 1.31(q31) format for all FFT sizes */
    /* Total process is divided into three stages */
    /* process first stage, middle stages, & last stage */

    /* Start of first stage process */

    /* Initializations for the first stage */
    n2 = fftLen;
    n1 = n2;
    /* n2 = fftLen/4 */
    n2 >>= 2u;
    i0 = 0u;
    ia1 = 0u;

    j = n2;

    do
    {

        /* input is in 1.31(q31) format and provide 4 guard bits for the input */

        /*  index calculation for the input as, */
        /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
        i1 = i0 + n2;
        i2 = i1 + n2;
        i3 = i2 + n2;

        /*  Butterfly implementation */
        /* xa + xc */
        r1 = (pSrc[2u * i0] >> 4u) + (pSrc[2u * i2] >> 4u);
        /* xa - xc */
        r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);

        /* xb + xd */
        t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);

        /* ya + yc */
        s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
        /* ya - yc */
        s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);

        /* xa' = xa + xb + xc + xd */
        pSrc[2u * i0] = (r1 + t1);
        /* (xa + xc) - (xb + xd) */
        r1 = r1 - t1;
        /* yb + yd */
        t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);
        /* ya' = ya + yb + yc + yd */
        pSrc[(2u * i0) + 1u] = (s1 + t2);

        /* (ya + yc) - (yb + yd) */
        s1 = s1 - t2;

        /* yb - yd */
        t1 = (pSrc[(2u * i1) + 1u] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
        /* xb - xd */
        t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);

        /*  index calculation for the coefficients */
        ia2 = 2u * ia1;
        co2 = pCoef[ia2 * 2u];
        si2 = pCoef[(ia2 * 2u) + 1u];

        /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
        pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) -
                         ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;

        /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
        pSrc[2u * i1 + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) +
                              ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;

        /* (xa - xc) - (yb - yd) */
        r1 = r2 - t1;
        /* (xa - xc) + (yb - yd) */
        r2 = r2 + t1;

        /* (ya - yc) + (xb - xd) */
        s1 = s2 + t2;
        /* (ya - yc) - (xb - xd) */
        s2 = s2 - t2;

        co1 = pCoef[ia1 * 2u];
        si1 = pCoef[(ia1 * 2u) + 1u];

        /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
        pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
                         ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;

        /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
        pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
                                ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;

        /*  index calculation for the coefficients */
        ia3 = 3u * ia1;
        co3 = pCoef[ia3 * 2u];
        si3 = pCoef[(ia3 * 2u) + 1u];

        /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
        pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
                         ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;

        /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
        pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
                                ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;

        /*  Twiddle coefficients index modifier */
        ia1 = ia1 + twidCoefModifier;

        /*  Updating input index */
        i0 = i0 + 1u;

    }
    while(--j);

    /* data is in 5.27(q27) format */
    /* each stage provides two down scaling of the input */


    /* Start of Middle stages process */

    twidCoefModifier <<= 2u;

    /*  Calculation of second stage to excluding last stage */
    for (k = fftLen / 4u; k > 4u; k >>= 2u)
    {
        /*  Initializations for the first stage */
        n1 = n2;
        n2 >>= 2u;
        ia1 = 0u;

        for (j = 0; j <= (n2 - 1u); j++)
        {
            /*  index calculation for the coefficients */
            ia2 = ia1 + ia1;
            ia3 = ia2 + ia1;
            co1 = pCoef[ia1 * 2u];
            si1 = pCoef[(ia1 * 2u) + 1u];
            co2 = pCoef[ia2 * 2u];
            si2 = pCoef[(ia2 * 2u) + 1u];
            co3 = pCoef[ia3 * 2u];
            si3 = pCoef[(ia3 * 2u) + 1u];
            /*  Twiddle coefficients index modifier */
            ia1 = ia1 + twidCoefModifier;

            for (i0 = j; i0 < fftLen; i0 += n1)
            {
                /*  index calculation for the input as, */
                /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
                i1 = i0 + n2;
                i2 = i1 + n2;
                i3 = i2 + n2;

                /*  Butterfly implementation */
                /* xa + xc */
                r1 = pSrc[2u * i0] + pSrc[2u * i2];
                /* xa - xc */
                r2 = pSrc[2u * i0] - pSrc[2u * i2];

                /* ya + yc */
                s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
                /* ya - yc */
                s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

                /* xb + xd */
                t1 = pSrc[2u * i1] + pSrc[2u * i3];

                /* xa' = xa + xb + xc + xd */
                pSrc[2u * i0] = (r1 + t1) >> 2u;
                /* xa + xc -(xb + xd) */
                r1 = r1 - t1;
                /* yb + yd */
                t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
                /* ya' = ya + yb + yc + yd */
                pSrc[(2u * i0) + 1u] = (s1 + t2) >> 2u;

                /* (ya + yc) - (yb + yd) */
                s1 = s1 - t2;

                /* (yb - yd) */
                t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
                /* (xb - xd) */
                t2 = pSrc[2u * i1] - pSrc[2u * i3];

                /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
                pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32u)) -
                                 ((int32_t) (((q63_t) s1 * si2) >> 32u))) >> 1u;

                /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
                pSrc[(2u * i1) + 1u] =
                    (((int32_t) (((q63_t) s1 * co2) >> 32u)) +
                     ((int32_t) (((q63_t) r1 * si2) >> 32u))) >> 1u;

                /* (xa - xc) - (yb - yd) */
                r1 = r2 - t1;
                /* (xa - xc) + (yb - yd) */
                r2 = r2 + t1;

                /* (ya - yc) +  (xb - xd) */
                s1 = s2 + t2;
                /* (ya - yc) -  (xb - xd) */
                s2 = s2 - t2;

                /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
                pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
                                 ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;

                /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
                pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
                                        ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;

                /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
                pSrc[(2u * i3)] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
                                   ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;

                /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
                pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
                                        ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
            }
        }
        twidCoefModifier <<= 2u;
    }
#else
    uint32_t n1, n2, ia1, ia2, ia3, i0, j, k;
    q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
    q31_t xa, xb, xc, xd;
    q31_t ya, yb, yc, yd;
    q31_t xa_out, xb_out, xc_out, xd_out;
    q31_t ya_out, yb_out, yc_out, yd_out;

    q31_t *ptr1;
    q31_t *pSi0;
    q31_t *pSi1;
    q31_t *pSi2;
    q31_t *pSi3;
    q63_t xaya, xbyb, xcyc, xdyd;

    /* input is be 1.31(q31) format for all FFT sizes */
    /* Total process is divided into three stages */
    /* process first stage, middle stages, & last stage */

    /* Start of first stage process */

    /* Initializations for the first stage */
    n2 = fftLen;
    n1 = n2;
    /* n2 = fftLen/4 */
    n2 >>= 2u;

    ia1 = 0u;

    j = n2;

    pSi0 = pSrc;
    pSi1 = pSi0 + 2 * n2;
    pSi2 = pSi1 + 2 * n2;
    pSi3 = pSi2 + 2 * n2;

    do
    {
        /*  Butterfly implementation */
        /* xa + xc */
        r1 = (pSi0[0] >> 4u) + (pSi2[0] >> 4u);
        /* xa - xc */
        r2 = (pSi0[0] >> 4u) - (pSi2[0] >> 4u);

        /* xb + xd */
        t1 = (pSi1[0] >> 4u) + (pSi3[0] >> 4u);

        /* ya + yc */
        s1 = (pSi0[1] >> 4u) + (pSi2[1] >> 4u);
        /* ya - yc */
        s2 = (pSi0[1] >> 4u) - (pSi2[1] >> 4u);

        /* xa' = xa + xb + xc + xd */
        *pSi0++ = (r1 + t1);
        /* (xa + xc) - (xb + xd) */
        r1 = r1 - t1;
        /* yb + yd */
        t2 = (pSi1[1] >> 4u) + (pSi3[1] >> 4u);
        /* ya' = ya + yb + yc + yd */
        *pSi0++ = (s1 + t2);

        /* (ya + yc) - (yb + yd) */
        s1 = s1 - t2;

        /* yb - yd */
        t1 = (pSi1[1] >> 4u) - (pSi3[1] >> 4u);
        /* xb - xd */
        t2 = (pSi1[0] >> 4u) - (pSi3[0] >> 4u);

        /*  index calculation for the coefficients */
        ia2 = 2u * ia1;
        co2 = pCoef[ia2 * 2u];
        si2 = pCoef[(ia2 * 2u) + 1u];

        /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
        *pSi1++ = (((int32_t) (((q63_t) r1 * co2) >> 32)) -
                   ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;

        /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
        *pSi1++ = (((int32_t) (((q63_t) s1 * co2) >> 32)) +
                   ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;

        /* (xa - xc) - (yb - yd) */
        r1 = r2 - t1;
        /* (xa - xc) + (yb - yd) */
        r2 = r2 + t1;

        /* (ya - yc) + (xb - xd) */
        s1 = s2 + t2;
        /* (ya - yc) - (xb - xd) */
        s2 = s2 - t2;

        co1 = pCoef[ia1 * 2u];
        si1 = pCoef[(ia1 * 2u) + 1u];

        /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
        *pSi2++ = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
                   ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;

        /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
        *pSi2++ = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
                   ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;

        /*  index calculation for the coefficients */
        ia3 = 3u * ia1;
        co3 = pCoef[ia3 * 2u];
        si3 = pCoef[(ia3 * 2u) + 1u];

        /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
        *pSi3++ = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
                   ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;

        /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
        *pSi3++ = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
                   ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;

        /*  Twiddle coefficients index modifier */
        ia1 = ia1 + twidCoefModifier;

    }
    while(--j);

    /* data is in 5.27(q27) format */
    /* each stage provides two down scaling of the input */


    /* Start of Middle stages process */

    twidCoefModifier <<= 2u;

    /*  Calculation of second stage to excluding last stage */
    for (k = fftLen / 4u; k > 4u; k >>= 2u)
    {
        /*  Initializations for the first stage */
        n1 = n2;
        n2 >>= 2u;
        ia1 = 0u;

        for (j = 0; j <= (n2 - 1u); j++)
        {
            /*  index calculation for the coefficients */
            ia2 = ia1 + ia1;
            ia3 = ia2 + ia1;
            co1 = pCoef[ia1 * 2u];
            si1 = pCoef[(ia1 * 2u) + 1u];
            co2 = pCoef[ia2 * 2u];
            si2 = pCoef[(ia2 * 2u) + 1u];
            co3 = pCoef[ia3 * 2u];
            si3 = pCoef[(ia3 * 2u) + 1u];
            /*  Twiddle coefficients index modifier */
            ia1 = ia1 + twidCoefModifier;

            pSi0 = pSrc + 2 * j;
            pSi1 = pSi0 + 2 * n2;
            pSi2 = pSi1 + 2 * n2;
            pSi3 = pSi2 + 2 * n2;

            for (i0 = j; i0 < fftLen; i0 += n1)
            {
                /*  Butterfly implementation */
                /* xa + xc */
                r1 = pSi0[0] + pSi2[0];

                /* xa - xc */
                r2 = pSi0[0] - pSi2[0];


                /* ya + yc */
                s1 = pSi0[1] + pSi2[1];

                /* ya - yc */
                s2 = pSi0[1] - pSi2[1];


                /* xb + xd */
                t1 = pSi1[0] + pSi3[0];


                /* xa' = xa + xb + xc + xd */
                pSi0[0] = (r1 + t1) >> 2u;
                /* xa + xc -(xb + xd) */
                r1 = r1 - t1;
                /* yb + yd */
                t2 = pSi1[1] + pSi3[1];

                /* ya' = ya + yb + yc + yd */
                pSi0[1] = (s1 + t2) >> 2u;
                pSi0 += 2 * n1;

                /* (ya + yc) - (yb + yd) */
                s1 = s1 - t2;

                /* (yb - yd) */
                t1 = pSi1[1] - pSi3[1];

                /* (xb - xd) */
                t2 = pSi1[0] - pSi3[0];


                /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
                pSi1[0] = (((int32_t) (((q63_t) r1 * co2) >> 32u)) -
                           ((int32_t) (((q63_t) s1 * si2) >> 32u))) >> 1u;

                /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
                pSi1[1] =

                    (((int32_t) (((q63_t) s1 * co2) >> 32u)) +
                     ((int32_t) (((q63_t) r1 * si2) >> 32u))) >> 1u;
                pSi1 += 2 * n1;

                /* (xa - xc) - (yb - yd) */
                r1 = r2 - t1;
                /* (xa - xc) + (yb - yd) */
                r2 = r2 + t1;

                /* (ya - yc) +  (xb - xd) */
                s1 = s2 + t2;
                /* (ya - yc) -  (xb - xd) */
                s2 = s2 - t2;

                /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
                pSi2[0] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
                           ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;

                /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
                pSi2[1] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
                           ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;
                pSi2 += 2 * n1;

                /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
                pSi3[0] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
                           ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;

                /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
                pSi3[1] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
                           ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
                pSi3 += 2 * n1;
            }
        }
        twidCoefModifier <<= 2u;
    }
#endif

    /* End of Middle stages process */

    /* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
    /* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
    /* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
    /* data is in 5.27(q27) format for the 16 point as there are no middle stages */


    /* Start of last stage process */


    /*  Initializations for the last stage */
    j = fftLen >> 2;
    ptr1 = &pSrc[0];

    /*  Calculations of last stage */
    do
    {
#ifndef ARM_MATH_BIG_ENDIAN
        /* Read xa (real), ya(imag) input */
        xaya = *__SIMD64(ptr1)++;
        xa = (q31_t) xaya;
        ya = (q31_t) (xaya >> 32);

        /* Read xb (real), yb(imag) input */
        xbyb = *__SIMD64(ptr1)++;
        xb = (q31_t) xbyb;
        yb = (q31_t) (xbyb >> 32);

        /* Read xc (real), yc(imag) input */
        xcyc = *__SIMD64(ptr1)++;
        xc = (q31_t) xcyc;
        yc = (q31_t) (xcyc >> 32);

        /* Read xc (real), yc(imag) input */
        xdyd = *__SIMD64(ptr1)++;
        xd = (q31_t) xdyd;
        yd = (q31_t) (xdyd >> 32);

#else

        /* Read xa (real), ya(imag) input */
        xaya = *__SIMD64(ptr1)++;
        ya = (q31_t) xaya;
        xa = (q31_t) (xaya >> 32);

        /* Read xb (real), yb(imag) input */
        xbyb = *__SIMD64(ptr1)++;
        yb = (q31_t) xbyb;
        xb = (q31_t) (xbyb >> 32);

        /* Read xc (real), yc(imag) input */
        xcyc = *__SIMD64(ptr1)++;
        yc = (q31_t) xcyc;
        xc = (q31_t) (xcyc >> 32);

        /* Read xc (real), yc(imag) input */
        xdyd = *__SIMD64(ptr1)++;
        yd = (q31_t) xdyd;
        xd = (q31_t) (xdyd >> 32);


#endif

        /* xa' = xa + xb + xc + xd */
        xa_out = xa + xb + xc + xd;

        /* ya' = ya + yb + yc + yd */
        ya_out = ya + yb + yc + yd;

        /* pointer updation for writing */
        ptr1 = ptr1 - 8u;

        /* writing xa' and ya' */
        *ptr1++ = xa_out;
        *ptr1++ = ya_out;

        xc_out = (xa - xb + xc - xd);
        yc_out = (ya - yb + yc - yd);

        /* writing xc' and yc' */
        *ptr1++ = xc_out;
        *ptr1++ = yc_out;

        xb_out = (xa - yb - xc + yd);
        yb_out = (ya + xb - yc - xd);

        /* writing xb' and yb' */
        *ptr1++ = xb_out;
        *ptr1++ = yb_out;

        xd_out = (xa + yb - xc - yd);
        yd_out = (ya - xb - yc + xd);

        /* writing xd' and yd' */
        *ptr1++ = xd_out;
        *ptr1++ = yd_out;

    }
    while(--j);

    /* output is in 11.21(q21) format for the 1024 point */
    /* output is in 9.23(q23) format for the 256 point */
    /* output is in 7.25(q25) format for the 64 point */
    /* output is in 5.27(q27) format for the 16 point */

    /* End of last stage process */
}
